Optimal Jackknife for Discrete Time and Continuous Time Unit Root Models

• Main Authors: CHEN, Ye, YU, Jun
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2011
• Subjects: Bias reduction; Variance reduction; Vasicek model; Long-span Asymptotics; Autoregression; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/1313; https://ink.library.smu.edu.sg/context/soe_research/article/2312/viewcontent/optimaljackknifing08.pdf
• Institution: Singapore Management University

Maximum likelihood estimation of the persistence parameter in the discrete time unit root model is known for su§ering from a downward bias. The bias is more pronounced in the continuous time unit root model. Recently Chambers and Kyriacou (2010) introduced a new jackknife method to remove the Örst order bias in the estimator of the persistence parameter in a discrete time unit root model. This paper proposes an improved jackknife estimator of the persistence parameter that works for both the discrete time unit root model and the continuous time unit root model. The proposed jackknife estimator is optimal in the sense that it minimizes the variance. Simulations highlight the performance of the proposed method in both contexts. They show that our optimal jackknife reduces the variance of the jackknife method of Chambers and Kyriacou by at least 10% in both cases.